FIN HEAT TRANSFER CLASS NOTES FOR
Fin is a solid extended surface or a combined conduction convection system. Heat is transferred by Conduction within the solid and by convection from the fin surface in a PERPENDICULAR direction to that of conduction. Finally heat is lost to the surroundings. Fins exponentially increase the rate of heat transfer by increasing the surface area without increase of primary surface area. This increased surface area reduces the convective resistance and increases the rate of heat transfer economically. The fins should have large surface area per unit volume (>700 m2/m3) with small gas flow passages with natural laminar flow for increased rate of heat transfer. It increases the heat exchange between two fluids which are separated by a sold surface as in home radiators and cooling system in cars.
PURPOSE OF A FIN: To increase heat transfer by increasing the surface area without increase of primary surface area. FIN involves both (CONDUCTIVE + CONVECTIVE) HEAT TRANSFER. . Finally it loses heat to the atmosphere.
HOW FINS INCREASE HEAT TRANSFER: Convection equation
q =h A dT Watts.
Undoubtedly heat transfer can be increased by increasing the
(i) temperature difference
(iii) the contact surface area of the object
ΔT can’t be increased because of fin base temperature and environment temperature are normally fixed. Convective heat transfer coefficient can be increasing by using a fan to blow air over the surface. However , this has not been practically possible to increase ‘h’. Thus it is not feasible to change the first two options. Therefore, increasing the surface area seems to be the only choice possible. ‘This can be easily and economically achieved by fins.
TYPE OF FINS / SHAPES OF FINS
(i)Fins of constant area of cross section like rectangular, circular, square and elliptical fins
(ii) Fins with varying area of cross section like triangular, trapezoidal , parabolic and conical
(iii) Plate fins and wound fins from the two types above
Fig. Types of fins
PURPOSE OF DESIGNING A FIN
Fin should be most effective. It should be able to transfer many times the heat as compared without fins. It should also be cost effective.
Write the assumption used in the analysis of heat transfer through fins.
Fin parameter is represented by the letter ‘m’. It is given by the relation given below
m = (h P/k Ac)0.5
h surrounding medium convective HT coefficient
P is the perimeter of the fin
k thermal conductivity of fin material
Ac cross sectional area of the fin if rectangular, Ac =b x t
Q. FIN EFFICIENCY FOR A SINGLE FIN
It is applicable for a single fin.
Ratio of the actual rate of heat transfer to the maximum rate of heat transfer through the fin. Maximum heat transfer occurs if the entire fin were at the base temperature.
The fin efficiency is ηf = actual q.fin/ q.max with base temperature all along the length
ηf = (PhAck)1/2(Tb–T )/hPL (Tb–T )
Finally ηf =1/mL
Fin efficiency will always be less than one. This is
because assuming the temperature throughout
the fin is at the base temperature would increase
the heat transfer rate.
PRACTICAL APPLICATIONS OF FINS
(i) Electric motors
(ii) Car radiators
(v) Internal Combustion engines
(ix) Air craft engines
(x) Economizers of steam power plants
(xii) In nature, the ears of Jackrabbits and Fennec Foxes act as fins to release heat from within their bodies.
Fin Performance Parameters
Description of Fin performance in three different ways
(i) Effectiveness of a single fin
(ii) Efficiency of a single fin
(iii)Overall efficiency of an array of fins
FIN EFFECTIVENESS OF A SINGLE FIN
It is applicable for a single fin. It is the ratio of heat transfer with fin to the rate to the heat transfer without fin. Thus it is greater than 1. Practically it should be at least greater than 2.3.
The formula for a fin of infinite length
Єf = q. with fin/ q.without fin= (P h Ac k)1/2(Tb–T)/ h Ac (Tb–T)
= (Pk/h Ac)1/2
Єf = (Pk/h Ac)1/2
Where Ac is the fin cross-sectional area
For a rectangular fin, P = 2B + 2 t and Ac = B t
Where B is width of fin and t is the thickness of fin
Now if the fin is thin, Neglect 2t as compared to 2B
Therefore P/Ac = 2B/B t=2/t
Єf = (2k/ht)1/2 = (1/Bi)0.5
Biot number, Bi for a fin
Less value of Biot number is desirable for more effectiveness.
Biot number will be less if h is small i.e. gas environment all around the fin.
Further, Biot number will be less if thermal conductivity k of fin material is high.
Biot number will be less if the thickness of fin is less i.e. fin is thin.
ASSUMPTIONS USED IN FIN ANALYSIS
One-dimensional steady state heat conduction
Homogeneous and isotropic fin material, k is constant
No internal heat generation
Uniform cross-sectional area
Uniform convective heat transfer coefficient h
Negligible contact thermal resistance
Always calculate Rate of heat transfer at the base of the fin
NOMENCLATURE OF FIN
Base of the fin or root of the fin: Where fin connects to the main body
Tip of the fin—The other free end of the fin
Ac is cross sectional area of the fin = b x t for a rectangular fin
As is the surface area of the fin= perimeter x length= (2b+2t) L
Fig. Details of a rectangular fin
DERIVATION OF BASIC DIFFERENTIAL EQUATION FOR FINS OF CONSTANT AREA OF CROSS SECTION
General partial equation for a fin is
d2θ/dx2 –m2 θ=0
where parameter m = (hP/kAc)0.5
θ is the temperature difference